Retire the correlation gate: the shared spectrum governs recovery

A controlled truncation refutes the project's central go/no-go rule.
Projecting the recovering synthetic fields to rank r holds the field
correlation at 0.902-0.929 while recovery moves 6.2% -> 12.9% -> 95.6%
across ranks 4, 8, 16. A field past the supposed 0.9 threshold recovers
13%, so correlation neither predicts nor forbids recovery and the width
of the shared spectrum is what moves it.

The gate becomes a joint condition on correlation and shared width,
measured by principal angles against a scene-shuffled null. Neither
suffices alone: 18 shared directions at 0.508 fails, 11 at 0.902 fails.

With the old gate retired, natural data was finally searched: 0.0000
against 0.0039 chance. The old verdict was right, its reasoning was not.

Also closes route D by measurement. rho_IT ~ sqrt(4 log N / N) rises as N
falls, and at N = 16 through 96 the deepest state a strong searcher
reaches is deeper than the truth in 3/3 replicates at every size.

Free gains: eigenvalue-weighted projection over a wide basis with
128-dim text vectors takes the correlation 0.656 -> 0.716 and shared
width 10 -> 16. Hubness refuted as an inflation hypothesis.

Moving the per-image segmentation eigendecomposition onto the GPU cut
batch time from 130s to 1.9s.

Co-Authored-By: Claude <noreply@anthropic.com>

1 files changed, 8 insertions, 0 deletions

diff --git a/logs/rank_causal.log b/logs/rank_causal.log
new file mode 100644
index 0000000..3635e3c
--- /dev/null
+++ b/logs/rank_causal.log
@@ -0,0 +1,8 @@
+rank=4     rho=0.9017  recovery=0.062  eff_rank=44.9
+rank=8     rho=0.9058  recovery=0.129  eff_rank=71.3
+rank=16    rho=0.9281  recovery=0.956  eff_rank=95.7
+rank=32    rho=0.9282  recovery=0.938  eff_rank=109.5
+rank=64    rho=0.9284  recovery=0.958  eff_rank=106.3
+rank=128   rho=0.9285  recovery=0.961  eff_rank=106.0
+rank=256   rho=0.9285  recovery=0.958  eff_rank=106.0
+{"chance": 0.00390625}